Kinetic Theory

This is a multiple choice answer as classified in NCERT Exemplar

(a) Pressure is inversely proportional to slope

So $\frac{p_1}{}$$\frac{p_{}}{}$$\frac{2_{}}{}=\frac{m_2}{m_1}\mathrm{<1}$

So p₁ > p₂

This is a multiple choice answer as classified in NCERT Exemplar

(c) The pressure inside the gas will be 

P= p_a+Mg/A

A= area of piston

P_a= atmospheric pressure

Mg = weight of piston

When temperature is increases

pV=nRT so volume increases at constant pressure.

This is a multiple choice answer as classified in NCERT Exemplar

(b) Boyle's law is applicable when temperature is constant

PV=nRT=constant

PV= constant

So pressure is inversely proportional to volume.

So process is called isothermal process.

This is a multiple choice answer as classified in NCERT Exemplar

(d) In an ideal gas when a molecules collides elastically with a wall, the momentum transferred to each molecule will be twice the magnitude of its normal momentum. For the face EFGH, it transfer only half of that.

This is a multiple choice answer as classified in NCERT Exemplar

(b) As the motion of the vessel as a whole does not affect the relative motion of the gas molecules with respect to the walls of the vessel, hence pressure of the gas inside the vessel, as conserved by us, on the ground remains the same.

This is a short answer type question as classified in NCERT Exemplar

Volume occupied by 1 mole = 1mole of the gas at NTP= 22400mL=22400cc

So number of molecules in 1cc of hydrogen= $\frac{6.023*{10}^{23}}{22400}=2.688*{10}^{19}$

H₂ is a diatomic gas, having a total of 5 degrees of freedom

So total degrees possesed by all the molecules

= 5 $*2.688$ $*{10}^{19}=1.344*{10}^{20}$

This is a short answer type question as classified in NCERT Exemplar

Number of helium = 5

T=7^oC=7+273=280K

(a) hence number of atoms = number of moles $*$ Avogadro's number

= $5*6.023*{10}^{23}=30.015*{10}^{23}=3*{10}^{24}$ atoms

(b) now average kinetic energy per molecule = 3/2 K_BT

= total internal energy

= $\frac{3}{2}{K}_{b}T*$ number of atoms

= $\frac{3}{2}*1.38*{10}^{-23}*280*3*{10}^{24}=1.74*{10}^{4}J$

This is a short answer type question as classified in NCERT Exemplar

When air is pumped, more molecules are pumped and boyle's law is staed for situation where number of molecules remains constant . in this case as the number of air molecules keep increases, hence mass change. Boyle's law is only applicable in situations, where number of gas molecule of remains fixed.

This is a short answer type question as classified in NCERT Exemplar

Radius = 1A^o

Volume of hydrogen molecules = 4/3 $\pi$ r³

= 4/3 (3.14) (10^-10)³ $\approx 4*{10}^{-30}$ m³

Number of moles of H₂ = mass/molecular mass=0.5/2=0.25

Molecules of H₂ present = number of moles of H₂ present $*6.023*{10}^{23}$

= 0.25 $*6.023*{10}^{23}$

So volume of molecules present = molecule number $*$ volume of each molecules

= 0.25 $*6.0233*{10}^{23}*4*{10}^{23}$

$\approx$ 6 $*{10}^{-7}m$ ³

P_iV_i= P_fV_f

V_{f $\left(\frac{P_i}{p_f}\right)V$} = _i= $\frac{1}{100}(3*{10}^{-2})$ ³

V_f= 2.7 $*{10}^{-7}m$ ³